Question

simplify the following [{(625)^-1/2}^-1/4]^2

Answer 1

5 is the value of $\bold{\left[\left\{(625)^{-\left(\frac{1}{2}\right)}\right\}^{-\left(\frac{1}{4}\right)}\right]^{2}}$

Given:

$\left[\left\{(625)^{-\left(\frac{1}{2}\right)}\right\}^{-\left(\frac{1}{4}\right)}\right]^{2}$

To find:

The value of $\left[\left\{(625)^{-\left(\frac{1}{2}\right)}\right\}^{-\left(\frac{1}{4}\right)}\right]^{2} = ?$

Solution:

To find the solution of the above question we first simplify the powers let us take 625 = A

$\left[\left\{(A)^{-\left(\frac{2}{2}\right)}\right\}^{-\left(\frac{1}{4}\right)}\right]^{2}$

Multiplying the power from the exterior and going into the interior we get

$2 \times-\frac{1}{4} \times-\frac{1}{2}=-\frac{1}{4}$

Therefore, the value of the power after multiplication we get the effective power $=-\frac{1}{4}$

Therefore, the power of A is $(A)^{-\left(\frac{1}{4}\right)}$ which means $(625)^{-\left(\frac{1}{4}\right)}$, therefore, the final answer is 5.

Hence, 5 is the value of$\bold{\left[\left\{(625)^{-\left(\frac{1}{2}\right)}\right\}^{-\left(\frac{1}{4}\right)}\right]^{2}.}$

Answer 2

Answer:

By simplifying the given equation we get the answer as 5.

Step-by-step explanation:

To simplify: $\left[\left\{(625)^{-\frac{1}{2}}\right\}^{\frac{1}{4}}\right]^{2}$, powers have to be multiplied

Consider the powers  $\left[\frac{-1}{2} \times \frac{-1}{4}\right]^{2}=\left[\frac{-1}{2} \times \frac{-1}{4}\right] \times 2$

$\begin{array}{l}{=\left[\frac{-1}{2} \times \frac{-1}{2}\right]=\frac{1}{4}} \\ {(625)^{\frac{1}{4}}=(5 \times 5 \times 5 \times 5)^{\frac{1}{4}}} \\ {=(5)^{4}\left(\frac{1}{4}\right)}\end{array}$

Therefore, $\left[\left\{(625)^{-\frac{1}{2}}\right\}^{\frac{1}{4}}\right]^{2}$ = 5